Summer 2021 undergraduate research programs (SPUR and REU)

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**Update as of 2/12/2021:  Due to the continuing and unknown duration of COVID-19 conditions, the university has decided that all course instruction and undergraduate research programs (including Math REU and SPUR Programs) will be offered in an online instructional and research format only for Summer 2021.


Summer 2021 Department of Mathematics Undergraduate Research Programs

REU PROGRAM - Research Experience for Undergraduates

SPUR PROGRAM - Summer Program for Undergraduate Research

These summer programs provide the opportunity for undergraduate students of mathematics to participate in leading-edge research.  This year, one project is designated "REU" and the other project is designated "SPUR."  The difference between REU and SPUR projects is the funding support that is available.

We welcome all students to apply including U.S., Permanent Resident, and International students whether your home institution is within the U.S. or outside the U.S.  Please read carefully the information below under details and support/costs.  Certain criteria apply for international students with their home institution outside the U.S.


PROJECT TITLE:  Theoretical aspects of deep learning

Directed by Alex Townsend, ( and Professor Yeona Kang, Howard University,

Project details/abstract:  Techniques in neural networks and deep learning are behind revolutionary advancements in the last decade, from facial recognition to playing world-class chess and protein folding. There is now a significant need for mathematical theory to keep up with practical success in this area. In this REU program, we will be studying the theoretical aspects of approximation power, convergence vs. stability, and frequency-biasing, when applied to neural networks. We will be particularly interested in how these techniques can be used in the context of learning differential equation models from data and medical imaging. This REU program is organized with Howard University. Undergraduates will be jointly mentored by Prof. Yeona Kang at Howard University. 


PROJECT TITLE:  Loop groups and Verlinde algebra

Directed by Yiannis Loizides, (

Project details:  This project will focus on some questions related to the loop group of SU(2): the space of 2 by 2 unitary matrices of determinant 1 whose entries are trigonometric polynomials. We will learn a bit about loop groups, Riemann surfaces, topological quantum field theory, and the Verlinde algebra (which links these things together). One aim will be to carry out calculations closely related to the Verlinde algebra, and to interpret the results in terms of the geometry of SU(2). Another aim will be to develop and implement methods for computing some invariants of "moduli spaces" associated to Riemann surfaces, and then to prove identities suggested by the examples. Previous exposure to abstract algebra, topology and maybe even representations of SU(2) would be helpful, though not essential.


WHEN:  Both the REU and SPUR Programs are 8 week programs that will run from June 7, 2021 – July 30, 2021

WHERE: Mathematics Department, Malott Hall, Cornell University, Ithaca, NY 14853-4201.  Note:  As stated above we are planning in-person instruction/research with potential to move online to be determined during the spring semester, which will be based on state and university guidelines.

SUPPORT/COSTS (see below for further information on expenses):

The REU project is supported by the NSF ( RTG Grant, so students who are U.S. citizens or permanent residents are eligible to apply, and if selected will receive funding support of $5,000.00 under this NSF grant.

Any student funding that is provided for the SPUR program comes from the Cornell Department of Mathematics.  To receive Cornell funding for SPUR you must be a Cornell student, but do not need to be a U.S. citizen or resident.  Cornell students may apply for departmental support of $3,500.00.  Non-Cornell students are welcome to apply and participate in the program, but there is no funding available. 

Cornell students participating in the REU Program that are not NSF funded may apply for departmental support of $3,500.00.  CU students do not need to be a U.S. Citizen or resident to apply for departmental support.

We welcome applications from all students including Cornell, non-Cornell, and international students (see below under International Students).  Those who apply to the programs as self-funded applicants will still be subject to the same competitive selection process.

Participants will arrange for their own housing.  The Math Department will assist with providing information on housing and contact information to make reservations.  Depending on the impacts of Covid housing may be restricted and limited on campus including the Coops, which are generally the preferred choice by REU and SPUR students.

After you are selected and accept you will be registered as a Cornell Student as follows:

  1. If you are accepted to either program and you are a student (US or non-US/International student) currently attending and enrolled at a U.S. academic institution in a full-time 4-year undergraduate degree program, you will be registered through Cornell Summer Session, and no fees apply.  At the end of the program you will receive an “S” for satisfactory completion of the program.
  2. International students with their home institution at a non-U.S. college/university are also registered through Cornell Summer Session, but under the umbrella of the IRIP Program (International Research Internship Program -  As stated above, we certainly welcome international students to apply!  The IRIP Program only applies to full-time international students who are currently registered and attending non-U.S. institutions and are coming directly from their international institution.  The IRIP Program also applies if you are an international student currently registered and attending a non-U.S. institution and are enrolled in an exchange program and conducting academic work at a U.S. institution.  International students accepted to the REU or SPUR programs will be self-funded, enrolled through Summer Session under the umbrella of IRIP, and will be required to pay an administrative fee and have adequate health insurance that is university compliant.  If you participate in-person and pay the administrative fee under the IRIP Program you will earn 6 credits - Satisfactory or Unsatisfactory (not a letter grade).  If you participate remotely and do not pay the administrative fee you will receive “S” for satisfactory completion.

IRIP Costs (Only applies if programs are held in-person):  The student is responsible for paying an administrative fee of $2,362.50 for summer 2021.  IRIP offers a scholarship that is 25% of the current summer extramural tuition rate for 6 credits.  Here is an example of the calculation:  Summer 2021 administrative fee = $1,575.00 tuition per credit x 25% x 6 credits = 2,362.50.

Health Insurance Requirements:

If programs are held in person:
There is a small health fee that is charged to domestic/international student participants that are enrolled in a full-time degree program at a U.S. institution, which is covered by the Math Department.  The plan this fee covers is limited.  Universities and colleges in the U.S. require all students to have adequate health insurance, and your current plan should be compliant. This also includes any U.S. based insurance plan that a student may have with their parent/guardian.  However, you should check that there is no lapse in coverage and that your plan will cover healthcare while you are at Cornell.  Cornell health insurance requirements can be found at, and you have the option to purchase Cornell SHP if you choose. The program SHP cost for Summer 2021 is $570.00. International students with their home institution outside the U.S. and who are participating under the IRIP Program will be charged $570 for the Cornell Student Health Plan (SHP).

If programs are remote:
There will be no health fee charged and SHP is not required for International students who are participating remotely in their home country. Cornell requires that all students have health insurance wherever they are studying.

Total in-person participation expenses:

    • IRIP Program Administrative fee = 2,362.50 – Only applies to International Students who fall under the IRIP Program, and only if the programs are in-person.
    • Health Insurance (Student Health Plan, SHP) = $570.00 – Only applies to students who do not meet Cornell health insurance requirements and if programs are held in-person.
    • Housing/living costs (applies to all REU/SPUR students) – housing can range from approximately $70.00 - $130.00/week depending single/double occupancy and where you stay.  Generally students stay in Coop Housing on campus, which is most affordable.  Coop housing will likely be limited for Summer 2021 due to the possibility of their being continued impacts and restrictions from Covid. There is other campus housing that would be available, but at a slightly higher cost (student housing dorms, etc.)  There is also off campus  housing and sublets that may be available, but again may be limited due to Covid.
    • Food and other miscellaneous living expenses.
**The above information on health insurance requirements is based on previous guidelines (except for the cost) and may be subject to change.  




To apply you will need the following:

  1. Statement about your background, educational goals, and your scientific interests.  Include whatever further information you consider relevant and be sure to include information about your computer experience.
  2. At least two letters of recommendation, which can be uploaded to the application portal.  The reference writer is notified to upload their letter once you enter their information on the application.
  3. Transcripts (unofficial transcripts are accepted), which can be uploaded to the application portal.

You can apply at by clicking this application link: REU/SPUR Application

The deadline to submit your application is February 27, 2021 and offers will be made on approximately March 5, 2021.  If you have comments, questions, or concerns please send e-mail to the SPUR and REU coordinator at  Note:  These deadlines have been slightly extended.  We will be reviewing applications slightly beyond the February 27th deadline, and offers will be made shortly after that.  We are also taking into consideration the impacts of power outages in parts of the south.  We plan to begin extending offers by the week of March 8th.


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